How do you graph the polar equation #r=-5+3costheta#?

1 Answer
A. S. Adikesavan
Jul 21, 2018

Invalid equation that does not produce any non-negative r. I have been honoring Socratic graphic utility as precise, particularly in discarding pixels, when #r < 0#.

Explanation:

Here, #r = - 5 + 3 cos theta in [ - 8, -2 ]#.

It is high time that, globally, the practice of marking

points for negative r is no longer continued..

Importantly, the century old statement

#If n is an even positive integer, the number of loops created by

#r = cos ntheta and r =sin ntheta# is 2n#

has to be understood as inclusive of n r-negative loops.

It is all rotations and revolutions

For any antipodal ( diametrically opposite ) points

( x. y ) and ( - x, - y), the polar coordinates shall be

#( r, theta ) and ( r, theta + pi )# or

#( r, theta ) and ( r, theta - pi )#, for the opposite sense of

rotation/revolution.

Forever, the length ( modulus ) of the position ( distance ) vector,

#r = sqrt ( x^2 + y^2 )>= 0#.

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